# Phase 8 Part C: Levels vs Differences and Cointegration

## 1. Panel Unit Root Tests

**Z₁**: Mean ADF t-statistic = -0.047. Reject unit root at 5%: 0/237 countries (0%).

**Real 10y yield**: Mean ADF t-statistic = -1.201. Reject unit root at 5%: 0/23 countries (0%).

**Real 3m rate**: Mean ADF t-statistic = -1.840. Reject unit root at 5%: 1/23 countries (4%).

## 2. Engle-Granger Cointegration (Country-by-Country)

Countries tested: 23

Reject no-cointegration at 5%: 11/23 (48%)

Mean EG t-statistic: -3.147

| Country | T | EG t-stat | Reject (5%) |
|---|---|---|---|
| MEX | 24 | -5.501 | Yes |
| KOR | 25 | -4.840 | Yes |
| CAN | 45 | -4.533 | Yes |
| NZL | 45 | -4.277 | Yes |
| JPN | 36 | -4.015 | Yes |
| ITA | 34 | -3.751 | Yes |
| ESP | 45 | -3.656 | Yes |
| SWE | 39 | -3.639 | Yes |
| IRL | 45 | -3.567 | Yes |
| FIN | 37 | -3.541 | Yes |
| AUT | 35 | -3.491 | Yes |
| GBR | 45 | -2.983 | No |
| DEU | 45 | -2.751 | No |
| AUS | 45 | -2.697 | No |
| USA | 45 | -2.557 | No |
| BEL | 45 | -2.406 | No |
| NLD | 44 | -2.309 | No |
| PRT | 32 | -2.279 | No |
| DNK | 38 | -2.218 | No |
| GRC | 28 | -2.171 | No |
| NOR | 40 | -1.970 | No |
| FRA | 45 | -1.696 | No |
| CHE | 45 | -1.524 | No |

## 3. Kao Pooled Residual ADF

Pooled ADF coefficient: -0.3338

Pooled t-statistic: -13.799

Conclusion: REJECT no-cointegration at 5% (one-sided).

## 4. First-Differenced Specification

N = 884, R² = 0.666

- d_Z_1: 1.977 (p = 0.929)
- d_Z_2: 0.093 (p = 0.974)
- d_Z_3: -0.007 (p = 0.950)

*First-differenced demographics are null, confirming the level effect is a slow-moving equilibrium rather than cyclical variation.*
